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Benoit's Bender

A cache by lpaulriddle Send Message to Owner Message this owner
Hidden : 11/29/2016
Difficulty:
4.5 out of 5
Terrain:
2.5 out of 5

Size: Size:   small (small)

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Geocache Description:

Cache is not at the posted coordinates! Solve the puzzle below to determine the location of the cache.


To solve this puzzle, you'll need to learn a little bit about the Mandelbrot Set. You'll also (likely) need to write a simple computer program. For that reason, I've given the puzzle a high difficulty rating. Once you've solved it, the find should be easy.

The Mandelbrot Set is a set of complex numbers. To determine whether a given number is in the set, you apply a formula to it, over and over.

When you plot the numbers on a grid, you get a beautiful fractal image:

Mandelbrot Set

In the above image, the black pixels represent numbers that are part of the Mandelbrot Set. The other pixels are colored according to how "close" the given number is to being part of the set; or in other words, how many times the formula needed to run on the number to determine that the number was not in the set.

When you zoom in on areas of the fractal, intricate details and patterns are revealed. The level of detail is actually infinite! Here's an example. A couple of others are included in the image gallery.

Mandelbrot Zoom 1

There are many apps and web sites which will let you zoom in on the Mandelbrot Set. If you are interested, I encourage you to check some of them out.

The Puzzle

The solution to this puzzle lies with the following set of complex numbers, which, perhaps uncoincidentally, are not part of the Mandelbrot Set:

  • -0.8 + 0.16i
  • -0.78 - 0.34i
  • 0.1 + 0.62i
  • 0.44 + 0.36i
  • 0.04 + 0.64i
  • 0.4 + 0.14i
  • -0.28 + 0.64i
  • -1.26 + 0.04i

Note: I used Python to create the puzzle, and I successfully beta-tested the solution with Python, Perl, Ruby, C, and Java. If you're using something else, and having issues getting correct coordinates, I would suggest giving one of these a try. Good Luck!

Congratulations to EntropyEndeavor for the quick FTF!!!


You can validate your puzzle solution with certitude.

Additional Hints (Decrypt)

[Puzzle #1] Onvybhg enqvhf = 2
[Puzzle #2] Svany pbbeqvangrf va gur sbez qq zz ff.ff
[Hide] Fgnaqvat qrnq gerr

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)



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